Link between objective function and performances
Hello,
I have a question regarding the heuristics at stake when solving a binary linear optimization program using Gurobi.
I have a vector X of N binary variables, and I want to minimize an objective function f(X) = c^T X while satisfying a set of M linear constraints, M > N. More precisely, f(X) is a weighted sum of three terms: f(X) = lambda_f * E_f(X) + lambda_c * E_c(X) + lambda_m * E_m(X). E_f, E_c and E_m are all linear. The constraints are for their part independent from the lambdas.
Depending on how these lambda weights are set, I observe dramatic differences regarding the performances of the Gurobi solver. Even a slight difference between two combinations of weights can multiply by 10, or even 100 the resolution time. Admittedly, tuning the lambdas modifies the coefficients of the objective function, but this is the only difference. The number of variables, and the constraints are unchanged. My question is, how to explain such a performance gap ?
Thanks in advance for your answers.
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